Practical midcourse sample size modification in clinical trials

Two-stage designs for cross-over bioequivalence trials

The topic of applying two-stage designs in the field of bioequivalence studies has recently gained attention in the literature and in regulatory guidelines. While there exists some methodological research on the application of group sequential designs in bioequivalence studies, implementation of adaptive approaches has focused up to now on superiority and non-inferiority trials. Especially, no comparison of the features and performance characteristics of these designs has been performed, and therefore, the question of which design to employ in this setting remains open. In this paper, we discuss and compare 'classical' group sequential designs and three types of adaptive designs that offer the option of mid-course sample size recalculation. A comprehensive simulation study demonstrates that group sequential designs can be identified, which show power characteristics that are similar to those of the adaptive designs but require a lower average sample size. The methods are illustrated with a real bioequivalence study example.

Efficacy and safety of 12 versus 48 months of dual antiplatelet therapy after implantation of a drug-eluting stent: the OPTImal DUAL antiplatelet therapy (OPTIDUAL) trial: study protocol for a randomized controlled trial

Background

Dual antiplatelet therapy with aspirin and thienopyridine is required after placement of coronary drug-eluting stents (DES) to prevent thrombotic complications. Current clinical guidelines recommend at least 6 to 12 months of treatment after a DES implantation, but it may be beneficial to apply dual antiplatelet therapy for a longer duration.

Methods/design

The optimal dual antiplatelet therapy (OPTIDUAL) study aims to compare the benefits and risks of dual antiplatelet therapy applied for either 12 or 48 months. We will examine the occurrence of major adverse cardiovascular and cerebrovascular events (MACCE) in patients undergoing percutaneous coronary intervention with DES for the treatment of coronary lesions. The OPTIDUAL study is an open-label multicenter, randomized, national trial that will include 1,966 patients treated with DES. All patients will be treated with dual antiplatelet therapy for 12 months (+/− 3). Then, patients with no MACCE or major bleeding will be randomized to receive either 36 additional months of clopidogrel plus aspirin or aspirin only. The primary end-point is the combination of death from all causes, myocardial infarction, stroke and major bleeding. The secondary end points include the individual components of the primary end-point, stent thrombosis, repeat revascularization of the treated vessel and minor bleeding.

Discussion

This randomized trial is designed to assess the benefits and safety of 12 versus 48 months of dual antiplatelet therapy in patients that receive a DES. We aim to determine whether substantial prolongation of clopidogrel (a thienopyridine) after DES implantation offers an advantage over its discontinuation.

Trial registration

ClinicalTrials.gov Identifier: NCT00822536

On efficient two-stage adaptive designs for clinical trials with sample size adjustment

Group sequential designs are rarely used for clinical trials with substantial over running due to fast enrollment or long duration of treatment and follow-up. Traditionally, such trials rely on fixed sample size designs. Recently, various two-stage adaptive designs have been introduced to allow sample size adjustment to increase statistical power or avoid unnecessarily large trials. However, these adaptive designs can be seriously inefficient. To address this infamous problem, we propose a likelihood-based two-stage adaptive design where sample size adjustment is derived from a pseudo group sequential design using cumulative conditional power. We show through numerical examples that this design cannot be improved by group sequential designs. In addition, the approach may uniformly improve any existing two-stage adaptive designs with sample size adjustment. For statistical inference, we provide methods for sequential p-values and confidence intervals, as well as median unbiased and minimum variance unbiased estimates. We show that the claim of inefficiency of adaptive designs by Tsiatis and Mehta ( 2003 ) is logically flawed, and thereby provide a strong defense of Cui et al. ( 1999 ).

Considerations in the rationale, design and methods of the Strategic Timing of AntiRetroviral Treatment (START) study

BACKGROUND

Untreated human immunodeficiency virus (HIV) infection is characterized by progressive depletion of CD4+ T lymphocyte (CD4) count leading to the development of opportunistic diseases (acquired immunodeficiency syndrome (AIDS)), and more recent data suggest that HIV is also associated with an increased risk of serious non-AIDS (SNA) diseases including cardiovascular, renal, and liver diseases and non-AIDS-defining cancers. Although combination antiretroviral treatment (ART) has resulted in a substantial decrease in morbidity and mortality in persons with HIV infection, viral eradication is not feasible with currently available drugs. The optimal time to start ART for asymptomatic HIV infection is controversial and remains one of the key unanswered questions in the clinical management of HIV-infected individuals.

PURPOSE

In this article, we outline the rationale and methods of the Strategic Timing of AntiRetroviral Treatment (START) study, an ongoing multicenter international trial designed to assess the risks and benefits of initiating ART earlier than is currently practiced. We also describe some of the challenges encountered in the design and implementation of the study and how these challenges were addressed.

METHODS

A total of 4000 study participants who are HIV type 1 (HIV-1) infected, ART naïve with CD4 count > 500 cells/µL are to be randomly allocated in a 1:1 ratio to start ART immediately (early ART) or defer treatment until CD4 count is <350 cells/µL (deferred ART) and followed for a minimum of 3 years. The primary outcome is time to AIDS, SNA, or death. The study had a pilot phase to establish feasibility of accrual, which was set as the enrollment of at least 900 participants in the first year.

RESULTS

Challenges encountered in the design and implementation of the study included the limited amount of data on the risk of a major component of the primary endpoint (SNA) in the study population, changes in treatment guidelines when the pilot phase was well underway, and the complexities of conducting the trial in a geographically wide population with diverse regulatory requirements. With the successful completion of the pilot phase, more than 1000 participants from 100 sites in 23 countries have been enrolled. The study will expand to include 237 sites in 36 countries to reach the target accrual of 4000 participants.

CONCLUSIONS

START is addressing one of the most important questions in the clinical management of ART. The randomization provided a platform for the conduct of several substudies aimed at increasing our understanding of HIV disease and the effects of antiretroviral therapy beyond the primary question of the trial. The lessons learned from its design and implementation will hopefully be of use to future publicly funded international trials.

The use of group sequential, information-based sample size re-estimation in the design of the PRIMO study of chronic kidney disease

BACKGROUND

Chronic kidney disease is associated with a marked increase in risk for left ventricular hypertrophy and cardiovascular mortality compared with the general population. Therapy with vitamin D receptor activators has been linked with reduced mortality in chronic kidney disease and an improvement in left ventricular hypertrophy in animal studies.

PURPOSE

PRIMO (Paricalcitol capsules benefits in Renal failure Induced cardia MOrbidity) is a multinational, multicenter randomized controlled trial to assess the effects of paricalcitol (a selective vitamin D receptor activator) on mild to moderate left ventricular hypertrophy in patients with chronic kidney disease.

METHODS

Subjects with mild-moderate chronic kidney disease are randomized to paricalcitol or placebo after confirming left ventricular hypertrophy using a cardiac echocardiogram. Cardiac magnetic resonance imaging is then used to assess left ventricular mass index at baseline, 24 and 48 weeks, which is the primary efficacy endpoint of the study. Because of limited prior data to estimate sample size, a maximum information group sequential design with sample size re-estimation is implemented to allow sample size adjustment based on the nuisance parameter estimated using the interim data. An interim efficacy analysis is planned at a pre-specified time point conditioned on the status of enrollment. The decision to increase sample size depends on the observed treatment effect. A repeated measures analysis model, using available data at Week 24 and 48 with a backup model of an ANCOVA analyzing change from baseline to the final nonmissing observation, are pre-specified to evaluate the treatment effect. Gamma-family of spending function is employed to control family-wise Type I error rate as stopping for success is planned in the interim efficacy analysis.

LIMITATIONS

If enrollment is slower than anticipated, the smaller sample size used in the interim efficacy analysis and the greater percent of missing week 48 data might decrease the parameter estimation accuracy, either for the nuisance parameter or for the treatment effect, which might in turn affect the interim decision-making.

CONCLUSIONS

The application of combining a group sequential design with a sample-size re-estimation in clinical trial design has the potential to improve efficiency and to increase the probability of trial success while ensuring integrity of the study.

Understanding the FDA guidance on adaptive designs: historical, legal, and statistical perspectives

The recent Food and Drug Administration (FDA) guidance for industry on adaptive designs is perhaps one of the important undertakings by CDER/CBER Office of Biostatistics. Undoubtedly, adaptive designs may affect almost all phases of clinical development and impact nearly all aspects of clinical trial planning, execution and statistical inference. Thus, it is a significant accomplishment for the Office of Biostatistics to develop this well-thought-out and all-encompassing guidance document. In this paper, we discuss some critical topical issues of adaptive designs with supporting methodological work from either existing literature, additional technical notes, or accompanying papers. In particular, we provide numerous sources of design, conduct, analysis, and interpretation bias that arise from statistical procedures. We illustrate, as a result, and caution that substantial research is necessary for many adaptive designs to meet required scientific standards prior to their applications in clinical trials.

The dual test: safeguarding p-value combination tests for adaptive designs

Many modern adaptive designs apply an analysis where p-values from different stages are weighted together to an overall hypothesis test. One merit of this combination approach is that the design can be made very flexible. However, combination tests violate the sufficiency and conditionality principles. As a consequence, combination tests may lead to absurd conclusions, such as 'proving' a positive effect while the average effect is negative. We explore the possibility of modifying the test so that such illogical conclusions are no longer possible. The dual test requires both the weighted combination test and a naïve test, ignoring the adaptations, to be statistically significant. The result is that the flexibility and type I error level control of the combination test are preserved, while the naïve test adds a safeguard against unconvincing results. The dual test is, by construction, at least as conservative as the combination test. However, many design changes will not lead to any power loss. A typical situation where the combination approach can be used is two-stage sample size reestimation (SSR). For this case, we give a complete specification of all sample size modifications for which the two tests are equally powerful. We also study the overall power loss for some suggested SSR rules. Rules based on conditional power generally lead to ignorable power loss while a decision analytic approach exhibits clear discrepancies between the two tests.

A Bayesian adaptive design for two-stage clinical trials with survival data

A randomized two-stage adaptive Bayesian design is proposed and studied for allocation and comparison in a phase III clinical trial with survival time as treatment response. Several exact and limiting properties of the design and the follow-up inference are studied, both numerically and theoretically, and are compared with a single-stage randomized procedure. The applicability of the proposed methodology is illustrated by using some real data.

Flexible design of two-stage adaptive procedures for phase III clinical trials

The recent popularity of two-stage adaptive designs has fueled a number of proposals for their use in phase III clinical trials. Many of these designs assign certain restrictive functional forms to the design elements of stage 2, such as sample size, critical value and conditional power functions. We propose a more flexible method of design without imposing any particular functional forms on these design elements. Our methodology permits specification of a design based on either conditional or unconditional characteristics, and allows accommodation of sample size limit. Furthermore, we show how to compute the P value, confidence interval and a reasonable point estimate for any design that can be placed under the proposed framework.

Adaptive Statistical Analysis Following Sample Size Modification Based on Interim Review of Effect Size

In designing a comparative clinical trial, the required sample size is a function of the effect size, the value of which is unknown and at best may be estimated from historical data. Insufficiency in sample size as a result of overestimating the effect size can be destructive to the success of the clinical trial. Sample size re-estimation may need to be properly considered as a part of clinical trial planning. This paper is intended to give the motivations for the sample size re-estimation based partly on the effect size observed at an interim analysis and for a resulting simple adaptive test strategy. The performance of this adaptive design strategy is assessed by comparing it with a fixed maximum sample size design that is properly adjusted in anticipation of the possible sample size adjustment.

The Use of Weighted Z-Tests in Medical Research

Traditionally the un-weighted Z-tests, which follow the one-patient-one-vote principle, are standard for comparisons of treatment effects. We discuss two types of weighted Z-tests in this manuscript to incorporate data collected in two (or more) stages or in two (or more) regions. We use the type A weighted Z-test to exemplify the variance spending approach in the first part of this manuscript. This approach has been applied to sample size re-estimation. In the second part of the manuscript, we introduce the type B weighted Z-tests and apply them to the design of bridging studies. The weights in the type A weighted Z-tests are pre-determined, independent of the prior observed data, and controls alpha at the desired level. To the contrary, the weights in the type B weighted Z-tests may depend on the prior observed data; and the type I error rate for the bridging study is usually inflated to a level higher than that of a full-scale study. The choice of the weights provides a simple statistical framework for communication between the regulatory agency and the sponsor. The negotiation process may involve practical constrains and some characteristics of prior studies.

Are Flexible Designs Sound?

Flexible designs allow large modifications of a design during an experiment. In particular, the sample size can be modified in response to interim data or external information. A standard flexible methodology combines such design modifications with a weighted test, which guarantees the type I error level. However, this inference violates basic inference principles. In an example with independent N(mu, 1) observations, the test rejects the null hypothesis of mu < or = 0 while the average of the observations is negative. We conclude that flexible design in its most general form with the corresponding weighted test is not valid. Several possible modifications of the flexible design methodology are discussed with a focus on alternative hypothesis tests.

Estimation in flexible two stage designs

Adaptive test designs for clinical trials allow for a wide range of data driven design adaptations using all information gathered until an interim analysis. The basic principle is to use a test statistics which is invariant with respect to the design adaptations under the null hypothesis. This allows for a control of the type I error rate for the primary hypothesis even for adaptations not specified a priori in the study protocol. Estimation is usually another important part of a clinical trial, however, is more difficult in adaptive designs. In this research paper we give an overview of point and interval estimates for flexible designs and compare methods for typical sample size rules. We also make some proposals for confidence intervals which have nominal coverage probability also after an unforeseen design adaptation and which contain the maximum likelihood estimate and the usual unadjusted confidence interval.

Operating characteristics of sample size re-estimation with futility stopping based on conditional power

Various methods have been described for re-estimating the final sample size in a clinical trial based on an interim assessment of the treatment effect. Many re-weight the observations after re-sizing so as to control the pursuant inflation in the type I error probability alpha. Lan and Trost (Estimation of parameters and sample size re-estimation. Proceedings of the American Statistical Association Biopharmaceutical Section 1997; 48-51) proposed a simple procedure based on conditional power calculated under the current trend in the data (CPT). The study is terminated for futility if CPT < or = CL, continued unchanged if CPT > or = CU, or re-sized by a factor m to yield CPT = CU if CL < CPT < CU, where CL and CU are pre-specified probability levels. The overall level alpha can be preserved since the reduction due to stopping for futility can balance the inflation due to sample size re-estimation, thus permitting any form of final analysis with no re-weighting. Herein the statistical properties of this approach are described including an evaluation of the probabilities of stopping for futility or re-sizing, the distribution of the re-sizing factor m, and the unconditional type I and II error probabilities alpha and beta. Since futility stopping does not allow a type I error but commits a type II error, then as the probability of stopping for futility increases, alpha decreases and beta increases. An iterative procedure is described for choice of the critical test value and the futility stopping boundary so as to ensure that specified alpha and beta are obtained. However, inflation in beta is controlled by reducing the probability of futility stopping, that in turn dramatically increases the possible re-sizing factor m. The procedure is also generalized to limit the maximum sample size inflation factor, such as at m max = 4. However, doing so then allows for a non-trivial fraction of studies to be re-sized at this level that still have low conditional power. These properties also apply to other methods for sample size re-estimation with a provision for stopping for futility. Sample size re-estimation procedures should be used with caution and the impact on the overall type II error probability should be assessed.

Estimation of a parameter and its exact confidence interval following sequential sample size reestimation trials

For confirmatory trials of regulatory decision making, it is important that adaptive designs under consideration provide inference with the correct nominal level, as well as unbiased estimates, and confidence intervals for the treatment comparisons in the actual trials. However, naive point estimate and its confidence interval are often biased in adaptive sequential designs. We develop a new procedure for estimation following a test from a sample size reestimation design. The method for obtaining an exact confidence interval and point estimate is based on a general distribution property of a pivot function of the Self-designing group sequential clinical trial by Shen and Fisher (1999, Biometrics55, 190-197). A modified estimate is proposed to explicitly account for futility stopping boundary with reduced bias when block sizes are small. The proposed estimates are shown to be consistent. The computation of the estimates is straightforward. We also provide a modified weight function to improve the power of the test. Extensive simulation studies show that the exact confidence intervals have accurate nominal probability of coverage, and the proposed point estimates are nearly unbiased with practical sample sizes.

A framework for two-stage adaptive procedures to simultaneously test non-inferiority and superiority

In clinical trials it is often desirable to test for non-inferiority and for superiority simultaneously. For such a situation a two-stage adaptive procedure may be advantageous to a conventional single-stage procedure because a two-stage adaptive procedure allows the design of stage II, including the main study objective and sample size, to depend on the outcome of stage I. We propose a framework for designing two-stage adaptive procedures with a possible switch of the primary study objectives at the end of stage I between non-inferiority and superiority. The framework permits control of the type I error rate and specification of the unconditional powers and maximum sample size for each of non-inferiority and superiority objectives. The actions at the end of stage I are predetermined as functions of the stage I observations, thus making specification of the unconditional powers possible. Based on the results at the end of stage I, the primary objective for stage II is chosen, and sample sizes and critical values for stage II are determined.